# Questions tagged [matching]

A matching (aka **Independent Edge Set**) in a simple graph is the set of pairwise non-adjacent edges i.e. no two edges have common vertex.

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### Hardness result for online matching

Currently studying the following paper: "Fair Allocation in Online Markets" - Gollapudi and Panigrahi 2014 In which they present Theorem 2 as a hardness result for online maxmin matchings (...
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### Can somebody please explain what are these variables doing here?

I have this algorithm: I understand overall what's happening here, we're shrinking the blossoms (odd cycles) to end up with a bipartite matching problem, and then opening them again to get a maximum ...
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### calculating the string similarity of an optimal alignment

description of the algorithms behavior I have two strings s1 and s2, with $len\_s1 <= len\_s2$. I would like to find the ...
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### Is there an approximation algorithm for the three-person stable roommates problem?

While there's an algorithm for solving the stable roommates problem, I understand that the three-people-per-room version of that problem, sometimes called the "threesome roommates problem", ...
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### Matching with specific cardinality

In a weighted graph $G(\mathcal{V},\mathcal{E})$ where $w(i,j)$ is the weight of the edge $(i,j) \in \mathcal{E}$. How can I find a maximum weighted matching with a specific size (i.e specific ...
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### Gale-Shapley Stable matching where one man's preference list changes

Given $n>1$ women and men. Let $M$ be the stable matching given by the Gale-Shapley algorithm with men proposing. Is there a stable matching instance such that: changing one man's preference list ...
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### Computing a fractional matching of maximum product in a bipartite graph

Given a bipartite graph $(X\cup Y, E)$ with edge weights, it is easy to find a matching in which the product of weights is maximum: replace each edge weight with its logarithm, and find a matching in ...
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### Maximum matching for general graph

I am studying the maximum matching problem and I was trying to understand why the classical augmenting path algorithm does not work for the general graph (i.e. for non bipartite graph) and you must ...
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### Can't wrap my head around on building a suffix table for Boyer Moore

My resources were the following video, as well as this video. Basically, in one of the videos they state that the good suffix table for the pattern "ABCBAB" is the following: k suffix d2 1 ...
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### Algorithm for b-matching on bipartite graph [duplicate]

I have a bipartite graph, where I want to assign nodes in Left set to Right set of nodes. There is a "b" constraint, which limits the maximum possible node degrees on the Right set. Since it is a ...